Adrawer contains 3 tank tops, 6 short-sleeve shirts, 4 three-quarter sleeve shirts, and 5 long-sleeve shirts. what is the probability of randomly choosing a tank top and then a three-quarter sleeve length, if you replace the tank top?
a. 7/18
b. 1/27
c. 2/3
d. 1/18

The probability of  choosing a tank top and then a three-quarter sleeve length is:

                         1/27

The drawer contains:

3 tank tops, 6 short-sleeve shirts, 4 three-quarter sleeve shirts, and 5 long-sleeve shirts.

Now the drawing is done with replacement.

Hence, the drawing in the second chance is independent of drawing in the second chance.

Hence, we know that when two events A and B are independent then,

P(A∩B)=P(A)×P(B)

Hence,

P( choosing a tank top and then a three-quarter sleeve length) is:

P(choosing tank top)× P(choosing a three-quarter sleeve shirt)

= (3/18) × (4/18)

= 1/27

           Hence, the probability is:

                 Option: B   (1/27)

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b